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University of Hawai`I at Mānoa Department of Economics Working Paper Series University of Hawai`i at Mānoa Department of Economics Working Paper Series Saunders Hall 542, 2424 Maile Way, Honolulu, HI 96822 Phone: (808) 956 -8496 www.economics.hawaii.edu Working Paper No. 20-7 Clubs, Coase, and the Role of Government By James Roumasset March 2020 Clubs, Coase, and the Role of Government James Roumasset1 Abstract As Ronald Coase and others have shown, deducing the appropriate role of government in the economy requires a comparative institutions approach. Trying to generalize from oversimplified specifications regarding transaction costs, according to whether exclusion is possible or not, is a futile exercise. An alternative to the Ostrom matrix is to distinguish private, club, and collective consumption goods according to their technical characteristics, specifically their degree of congestabiilty. The other box of the Ostrom matrix, “common pool” resources, can also be usefully analyzed from a club perspective. Spillover goods are spatial clubs. Lastly, a version of the Coase theorem is offered that provides the foundation of comparative institutional analysis JEL classification: H4 Keywords: Public goods, club goods, congestability, Ostrom matrix, comparative institutions Public goods and the Coase Theorem are two of the most confusing parts of any text or curriculum about public economics. At least some of the confusion can be resolved by applying the concept of the shrinking core and by more clearly separating first-best efficiency conditions from second-best matters of implementation. The resulting framework helps to clarify the role of government in an economy. Public Goods It is commonplace to define public goods by the characteristics of non-rivalry and non- excludability. This tradition was established by Musgrave (1939), who even Samuelson described as “undoubtedly the authority in the whole field of public finance” (Desmarais-Tremblay 2017). Yet non- excludability is not featured in Samuelson’s “The Pure Theory of Public Expenditure” (1954). Musgrave eventually acceded to the primacy of non-rivalry (Musgrave 1969 and Desmarais-Tremblay 2017) but nonetheless helped to promulgate the now famous two-by-two taxonomy of goods according to rivalry in consumption and the feasibility of exclusion (Musgrave and Musgrave 1973, hereafter M&M). In M&M’s 2x2 diagram, the rows are labeled rival and non-rival and the columns according to whether exclusion is feasible or not. Ostrom and Ostrom (1977) named M&M’s four categories as: 1. Rival/Excludable: Private Good 2. Rival/Non-excludable: Common Pool Resource 3. Non-rival/Excludable: Toll Good (changed to Club Good e.g. in Ostrom 1990) 1Graduate School for International Development and Cooperation, Hiroshima University; Economics Department, University of Hawaii; and University of Hawaii Economic Research Organization. Thanks to Noel de Dios for inspiration and support and to Lee Endress, Nori Tarui, and an anonymous referee for helpful comments. 4. Non-rival/Non-excludable: Public Good Similar diagrams appear in many textbooks,2 in spite of Samuelson’s objections. The problem with the names is that they conflate the characteristics of the good with organizational form. As Coase (e.g. 1937, 1960, and 2012) famously explained, however, different organizational forms are capable of achieving the same efficient solution absent transaction costs (see also Arrow 1969). Therefore, there is no unique mapping from good characteristics to the optimal mode of provision. Monitoring, enforcement, and other transaction costs must be considered in tandem with characteristics of the good to determine which organizational form is appropriate for which good in what transaction cost environment. For example, natural resources, whose stock is given by nature and may be depleted over time, can, under different transaction cost conditions, be efficiently organized as private property, central government management, common property (res communes), and even no property (res nullius).3 Samuelson (1954) found non-excludability unnecessary for his derivation of efficiency conditions and tried on multiple occasions to convince Musgrave to drop exclusion from his taxonomy.4 His formalization of non-rivalry has the total quantity of the good produced as an argument in the utility function of all individuals, leading him to use the term “collective consumption good” instead of “public good,” and rendering non-excludability redundant. This does not mean that excludability is irrelevant, but its relevance is manifested at a different level of analysis, one with transaction costs.5 Excludability, a feature of property rights, is just one of many possible enforcement mechanisms. Collective Consumption, Clubs, and Congestability As an alternative to the Musgrave-Ostrom matrix,6 we seek a classification of public, private and club goods that is independent of transaction cost issues such as excludability. To that end, we can subsume collective-consumption and private goods as special cases of club goods according to their degree of congestability. Club goods are characterized by congestion as new members are added to the club. Collective-consumption goods are the limiting case of club goods where congestion costs are zero. Private goods represent the other polar extreme of club goods, where congestion costs of one consumer are so high as to be strictly subtractive, i.e. another consumer’s consumption of the good reduces mine to zero (Smith 2014). In his original theory of clubs, Buchanan (1965) considered a club good of fixed size, e.g. a swimming pool, and defined optimal club membership as that number that minimizes the sum of long- 2 See e.g. Hindriks and Myles (2013). Categories 2 and 3 are sometimes called “impure public goods”. 3 See the penultimate section, Common Property Resources. 4 Desmarais-Tremblay (2017) details the intellectual history of public goods, including discussions and correspondence between Musgrave and Samuelson. Musgrave (1969) accepted the primacy of Samuelson’s jointness in consumption over non-excludability on the grounds that even if tolling is possibly on an uncrowded bridge, exclusion would be inefficient, i.e. the optimal toll would be zero. Musgrave and Musgrave (1973) also qualify their two-by-two diagram, noting: “It is customary, however to reserve the term for case 3 and 4, i.e., situations of nonrival consumption” (as quoted in Desmarais-Tremblay 2017). See also Samuelson (1969) for an elaboration of his earlier views. 5 See e.g. Roumasset (1978) and Dixit (1999) on the 1st, 2nd, and 3rd-best levels of analysis. 6 See de Dios (2015) for an extension of the Ostrom two-by-two table to a two-by-three table including externalities. run capital and operating costs plus congestion costs (lost benefits), both per member. The number of competing clubs is then given by the number of potential members (e.g. population) divided by the optimal membership size. While not using the same terminology, Tiebout (1956) asserted that consumer mobility and competition between clubs would then lead to an efficient solution with homogenous membership in each club. This led him to conclude that decentralized pricing is hypothetically capable of achieving efficiency, despite Samuelson’s (1954) assertion to the contrary. Extending Buchanan’s (1965) theory to the case of endogenous production, the club model can be derived as follows. The utility of an individual member is given by U(Y,S,n), where Y is consumption of the numeraire good, S, is production and consumption of the club/social good, and n is number of members in the club. The consumer spends her endowment, Y0, on Y and her contribution to S, C(S)/n. The necessary condition for optimality with respect to the quantity of the social good in each club is that the aggregate marginal benefit of the club’s membership is equal to the marginal cost of producing the good, i.e. nUS/UY = MCs, the well-known Samuelson condition. The condition for the optimal number of members in a club is that the marginal benefit of adding an additional member is equal to its marginal cost. The marginal benefit to a representative member is the marginal cost reduction per person. The 2 7 marginal cost is the increased congestion cost, i.e. C(S)/n = -Un/UY. The greater the marginal disutility of congestion, the smaller is optimal club size. If C(S*) ≤ -Un/UY for any n ≥ 1, then we have a corner solution with one member per club, i.e. a private good.8 If there is no congestion such that the marginal disutility of an additional member is zero, the efficiency conditions call for the opposite polar extreme: one club optimally serving the entire population. We can therefore classify goods entirely based on congestion costs. Private and collective-consumption goods represent the two polar extremes of prohibitive congestion and no congestion. While these extremes are formally special cases of club goods, it is convenient to think of club goods as the intermediate category where there is an internal solution and the optimal number of clubs is between one and the number of consumers. Only in turning to questions of implementation do we find a role for exclusion. If clubs are able to enforce payment by the mechanism of exclusion, then they can compete for membership. As the population divided by the number of consumer types increases, the set of undominated solutions (the core of the economy) shrinks to the Lindahl equilibrium with homogeneous membership in each of the clubs. With constant returns to scale this is achieved with members of each club paying an equal share of the costs, thereby proving the Tiebout hypothesis (Wooders 1980 and 1989, Conley and Wooders 2010). Clubs are typically conceived as voluntary associations, although the Tiebout proposition was 7 Note that the derivative (with respect to n) of the cost per member, C(S)/n, is -C(S)/n2. Since the additional cost is negative, the cost reduction (benefit) is positive, i.e.
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